....I don't quite rank TFA before ANH, but if I can try explaining some reason why I *enjoy* it more personally...
I love Finn. I love his character arc. I love the way he remains a largely baseline human and soldier, even if background material says he's a top tier rookie Stormtrooper; he doesn't miss as much as regular Stormtroopers, but he's not a deadeye or a phenomenal ace pilot, and when equipped with an unfamiliar weapon, he can be defeated by an opponent using one they're familiar with. He's the nameless, faceless background henchmen who people have made fun of since the 80's. Except...
He decides he won't be a murderer. Initially, that's it. It's not even really heroic, it's simple human decency. But he's not an idiot, so he effects an escape plan with a prisoner. In return, he gets transport off his ship, gets a name, and a cool jacket. Then, still on the run as a desperate deserter, he realizes his very presence has put two beings in danger, and accepts some responsibility for their safety, and, as a matter of convenience and perhaps a bit of compassion, fulfills his "dead" escape partner's missions. So he's gotten a bit more heroic, but only a bit; he's still mostly a pragmatic anti-Hero.
But when he sees the Hosnian System go up, even after getting his ride off into the underworld and away from the First Order, he feels some compulsion to inform Han Solo what happened, postponing or canceling his escape for a while. Then he finds out Rey's unaccounted for, and he silently decides to stay and try and defend Maz Kanata's castle. It's probably for the sake of his friend Rey, since she's saved his life multiple times and he probably feels protective of his friends, since he lost two already that day. Still... The deserter abandoned his escape attempt and stood his ground against the First Order because he feels it's the right thing to do; that lie he told Poe is now uncomfortably true. Then he sees Rey get captured; his priorities immediately change, and he goes from just a deserter to a true defector.
Now, he wheels and deals himself onto a commando mission into the heart of the First Order's power to save his friend. He's still thinking fairly selfishly about his friend first, but he is heroic now. And he can prioritize the mission objective before his own; the rookie Stormtrooper given custodial chores dooms Starkiller Base by helping to lower the shield and blow up the bunker cover for the Base's weak spot. He has now become a "big deal" with the Resistance, just like the lie he told and then confessed to Rey. And while Rey ends up being Kylo's opposite number Force-wise, Finn's confrontation with the dark side brat over his friend's unconscience form shows him as the true foil to Kylo Ren: the nobody muggle who wasn't trying to save the day has thoroughly ruined the high strung, self important and insecure Kylo's objectives, and while totally outmatched by Kylo, still charges him dedicated to his attack, while the emotionally turbulent Kylo toys with him...and pays the price, because Finn's delayed long enough for his friend to reawaken and take up the saber.
I like other elements of TFA as well, but personally? I like Finn's story in TFA more than any other one in a single movie during Star Wars, and I think it's the most powerful "ordinary person becomes a hero" story in the franchise.